Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization | Paper Citation Record

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This paper cites A phase field model for isothermal crystallization of oxide melts.

Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization A phase field model for isothermal crystallization of oxide melts

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This paper cites Two- scale FE–FFT- and phase-field-based computational modeling of bulk microstruc- tural evolution and macroscopic material behavior.

Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Two- scale FE–FFT- and phase-field-based computational modeling of bulk microstruc- tural evolution and macroscopic material behavior

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This paper cites Three-Dimensional Landau Theory for Multivari- ant Stress-Induced Martensitic Phase Transformations. I. Austenite↔Martensite.

Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Three-Dimensional Landau Theory for Multivari- ant Stress-Induced Martensitic Phase Transformations. I. Austenite↔Martensite

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This paper cites Undercooling versus stress induced martensitic phase transformation: The case of MgO – partially stabilized zirconia.

Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Undercooling versus stress induced martensitic phase transformation: The case of MgO – partially stabilized zirconia

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This paper cites Modelling of laminated microstructures in stress- induced martensitic transformations.

Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Modelling of laminated microstructures in stress- induced martensitic transformations

Reference 6

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This paper cites A Phase-Field Study of Martensite Formation in Fe–Mn–Al–Ni Shape Memory Alloys as Caused by Nanoscale B2-Ordered Precipitate and Matrix Phase Interplay.

Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization A Phase-Field Study of Martensite Formation in Fe–Mn–Al–Ni Shape Memory Alloys as Caused by Nanoscale B2-Ordered Precipitate and Matrix Phase Interplay

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This paper cites Aphasefieldmodelforrate-independent crack propagation: Robust algorithmic implementation based on operator splits.

Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Aphasefieldmodelforrate-independent crack propagation: Robust algorithmic implementation based on operator splits

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This paper cites A continuum phase field model for fracture.

Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization A continuum phase field model for fracture

Reference 10

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization A simple and unified implementation of phase field and gradient damage models

Reference 11

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This paper cites A phase field formulation for hydrogen assisted cracking.

Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization A phase field formulation for hydrogen assisted cracking

Reference 12

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Observation 7c88cbd5-da02-4786-bd92-37b6f859d8eb · outbound

This paper cites Finite-DeformationPhase-FieldChemo- mechanics for Multiphase, Multicomponent Solids.

Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Finite-DeformationPhase-FieldChemo- mechanics for Multiphase, Multicomponent Solids

Reference 13

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Observation 223c5f4c-dcab-4fae-a48a-93a83a82dc36 · outbound

This paper cites Cahn-Hilliard Phase Field Theory Coupled to Mechanics: Fundamentals, Numerical Implementation and Application to Topol- ogy Optimization.

Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Cahn-Hilliard Phase Field Theory Coupled to Mechanics: Fundamentals, Numerical Implementation and Application to Topol- ogy Optimization

Reference 14

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This paper cites Chemo- Mechanical Phase-Field Modeling of Iron Oxide Reduction with Hydrogen.

Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Chemo- Mechanical Phase-Field Modeling of Iron Oxide Reduction with Hydrogen

Reference 15

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This paper cites Phase-Field Modeling of Hydrogen-Promoted Fracture: Natural Incorporation of Hydrostatic Stress Dependencies via a Chemical Potential-Based Variational Formulation.

Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Phase-Field Modeling of Hydrogen-Promoted Fracture: Natural Incorporation of Hydrostatic Stress Dependencies via a Chemical Potential-Based Variational Formulation

Reference 16

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This paper cites The Phase-Field Method in Optimal Design.

Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization The Phase-Field Method in Optimal Design

Reference 17

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This paper cites A phase field model for stress-based evolu- tion of load-bearing structures. Stress based evolution of load-bearing structures.

Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization A phase field model for stress-based evolu- tion of load-bearing structures. Stress based evolution of load-bearing structures

Reference 18

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This paper cites Phase-Field Models for Microstructure Evolution.

Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Phase-Field Models for Microstructure Evolution

Reference 19

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This paper cites Anintroductiontophase-fieldmodeling of microstructure evolution.

Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Anintroductiontophase-fieldmodeling of microstructure evolution

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Phase-fieldmodelsinmaterialsscience

Reference 21

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This paper cites Free Energy of a Nonuniform System. I. Interfacial Free Energy.

Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Free Energy of a Nonuniform System. I. Interfacial Free Energy

Reference 23

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This paper cites Homogeniza- tion methods and multiscale modeling: Nonlinear problems.

Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Homogeniza- tion methods and multiscale modeling: Nonlinear problems

Reference 24

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This paper cites A comparison of classical phenomenological, hybrid neural network, and high performance ROM FE2 models for open-cell foams: efficiency, accuracy, and flexibility.

Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization A comparison of classical phenomenological, hybrid neural network, and high performance ROM FE2 models for open-cell foams: efficiency, accuracy, and flexibility

Reference 26

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization FE 2 computationalhomog- enization for the thermo-mechanical analysis of heterogeneous solids

Reference 27

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This paper cites Computationalhomogenisationofthermo-viscoplastic composites: Large strain formulation and weak micro-periodicity.

Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Computationalhomogenisationofthermo-viscoplastic composites: Large strain formulation and weak micro-periodicity

Reference 28

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This paper cites Computational homoge- nization of piezoelectric materials using FE2 to determine configurational forces.

Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Computational homoge- nization of piezoelectric materials using FE2 to determine configurational forces

Reference 29

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Two-scale computational homogeniza- tionofelectro-elasticityatfinitestrains

Reference 30

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization FE2 simulations of magnetorheological elastomers: influence of microscopic boundary conditions, microstructures and free space on the macroscopic responses of MREs

Reference 31

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This paper cites A micromorphic computational homogenization frame- work for heterogeneous materials.

Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization A micromorphic computational homogenization frame- work for heterogeneous materials

Reference 32

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This paper cites Micromor- phic Computational Homogenization for Mechanical Metamaterials with Pattern- ing Fluctuation Fields.

Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Micromor- phic Computational Homogenization for Mechanical Metamaterials with Pattern- ing Fluctuation Fields

Reference 33

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This paper cites Direct FE2 modeling of heteroge- neous materials with a micromorphic computational homogenization framework.

Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Direct FE2 modeling of heteroge- neous materials with a micromorphic computational homogenization framework

Reference 34

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Micromorphic FE2 Simulation of Plastic Deformations of Foam Structures

Reference 35

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Computation of Non-Linear Magneto-Electric Product Properties of 0-3 Com- posites

Reference 36

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization An FE2-scheme for magneto-electro- mechanically coupled boundary value problems

Reference 37

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Phase-field elasticity model based on mechanical jump conditions

Reference 39

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This paper cites Homogenization of vis- coplastic constitutive laws within a phase field approach.

Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Homogenization of vis- coplastic constitutive laws within a phase field approach

Reference 40

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization A Numerical Convergence Study Regarding Homogenization Assumptions in Phase Field Modeling

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This paper cites Anefficientandquantitativephase-field model for elastically heterogeneous two-phase solids based on a partial rank-one homogenization scheme.

Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Anefficientandquantitativephase-field model for elastically heterogeneous two-phase solids based on a partial rank-one homogenization scheme

Reference 42

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization A gradient regularized model for shape memory alloys

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Observation cfa21592-d63d-4f5f-97dc-dab1f790f72a · outbound

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Homogenization of Phase Transforming Materials: The Concept of Phase-Morphology and Variable Scale Separations

Reference 44

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This paper cites A phase field approach for damage propagation in periodic microstructured materials.

Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization A phase field approach for damage propagation in periodic microstructured materials

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This paper cites A numerical-homogenization based phase-field fracture modeling of linear elastic heterogeneous porous media.

Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization A numerical-homogenization based phase-field fracture modeling of linear elastic heterogeneous porous media

Reference 46

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This paper cites Development and Calibration of a Phe- nomenological Material Model for Steel-Fiber-Reinforced High-Performance Con- crete Based on Unit Cell Calculations.

Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Development and Calibration of a Phe- nomenological Material Model for Steel-Fiber-Reinforced High-Performance Con- crete Based on Unit Cell Calculations

Reference 47

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This paper cites Multi-Phase-Field Method for Dynamic Fracture in Compos- ite Materials Based on Reduced-Order-Homogenization.

Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Multi-Phase-Field Method for Dynamic Fracture in Compos- ite Materials Based on Reduced-Order-Homogenization

Reference 48

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This paper cites Amultiscaleanisotropicpolymernetworkmodelcoupledwithphasefieldfracture.

Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Amultiscaleanisotropicpolymernetworkmodelcoupledwithphasefieldfracture

Reference 49

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This paper cites Asymptotic homogenization of phase- field fracture model: An efficient multiscale finite element framework for anisotropic fracture.

Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Asymptotic homogenization of phase- field fracture model: An efficient multiscale finite element framework for anisotropic fracture

Reference 50

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Size Effects in Martensitic Microstruc- tures: Finite-Strain Phase Field Model Versus Sharp-Interface Approach

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization GeneralizedGinzburg-LandauandCahn-Hilliardequationsbasedon a microforce balance

Reference 52

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Elastic properties of reinforced solids: Some theoretical principles

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This paper cites Diffusion and dispersion in porous media.

Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Diffusion and dispersion in porous media

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Some Applications of the Homogenization Theory

Reference 55

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Cosserat overall modeling of heterogeneous materials

Reference 56

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Generalized continua and non-homogeneous boundary conditions in homogenisation methods

Reference 57

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization On multiscale FE analyses of heterogeneous structures: from homogenization to multigrid solvers

Reference 58

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Minimal loading conditions for higher order numerical homogenisation schemes

Reference 59

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Homogenization of a Cauchy continuum towards a micromorphic con- tinuum

Reference 60

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Nonlocal reaction—diffusion equations and nu- cleation

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization A numerical two-scale homogenization scheme: the FE2-method

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization A Review of FE-FFT-Based Two-Scale Methods for Computational Modeling of Microstruc- ture Evolution and Macroscopic Material Behavior

Reference 64

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Direct FE2 for concurrent multilevel mod- elling of heterogeneous structures

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Interface propagation and microstruc- ture evolution in phase field models of stress-induced martensitic phase transfor- mations

Reference 66

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This paper cites An efficient FE-implementation of implicit gradient-enhanced damage models to simulate ductile failure.

Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization An efficient FE-implementation of implicit gradient-enhanced damage models to simulate ductile failure

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening

Reference 68

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Theoryofphase-orderingkinetics

Reference 69

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Metastable patterns in solutions ofut =ϵ 2uxx −f(u)

Reference 70

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Unresolved cited work

Reference 71

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This paper cites A Reduced Order Model for a Stable Embedded Boundary Parametrized Cahn–Hilliard Phase-Field System Based on Cut Finite Elements.

Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization A Reduced Order Model for a Stable Embedded Boundary Parametrized Cahn–Hilliard Phase-Field System Based on Cut Finite Elements

Reference 72

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Reduced order methods for the solution of solidification Phase- Field models

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Extraction of reduced-order process-structure linkages from phase-field simulations

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks

Reference 75

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Self-adaptive physics-informed neural networks

Reference 76

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization PF-PINNs: Physics-informed neural networks for solving coupled Allen-Cahn and Cahn-Hilliard phase field equa- tions

Reference 77

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Deep learning for simulating the evolution of condensed matter systems at the continuum scale: methods and applications

Reference 78

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Scale-Bridging Phase-Field Modeling of Microstructure Evolution by FE$^2$ Computational Homogenization Generalized Continua

Reference 79

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